Inversion-symmetric electron gases as platforms for topological planar Josephson junctions

Intrinsic Rashba spin-orbital coupling (SOC) can exist in centrosymmetric materials with local inversion symmetry breaking. Here we show that such a SOC can induce topological superconductivity together with an in-plane Zeeman field in planar Josephson junctions formed by the centrosymmetric materials. A single Majorana mode can be created at each end of the junction. We demonstrate this result in a model respecting the same symmetry group with the iron-based superconductors. We derive the necessary Fermi surface condition for the topological planar junction and calculate the topological phase diagram with respect to the in-plane Zeeman field and the phase difference between the two superconductors. We provide experimental characteristics for the topological superconductivity, including the differential conductance and the Fano factor tomography which can be measured in the scanning tunneling spectroscopy. Our study reveals that the centrosymmetric systems with local-inversion-symmetry breaking can serve as new platforms for the topological planar Josephson junctions and helps to find more experimentally feasible materials for the topological superconductors.